Continuation and bifurcation analysis of dynamical systems

  • lectures by Davide Liessi
  • 18–26 February 2025
  • Sala riunioni, DMIF; Microsoft Teams

Program

The evolution of a phenomenon in time can usually be described mathematically as a dynamical system. The simplest objects of interest of the theory are equilibria, their stability properties and how they change when parameters vary, possibly undergoing bifurcations (i.e., qualitative changes in the landscape). A particularly effective approach to the problem is numerical continuation, a technique to compute curves which can be applied to equilibria moving in the parameter–state space.

In this course we will explore some of the main concepts and numerical techniques relevant to the theory of dynamical systems: from equilibria to periodic orbits to strange attractors and chaotic dynamics; from ordinary to delay and partial differential equations. A useful tool in our exploration will be the MATLAB-based MatCont package (https://sourceforge.net/projects/matcont/), which implements the methods we will study in a unified framework.

The University of Udine provides free access to MATLAB to students and personnel via the MATLAB campus-wide license.

Prerequisites

Basic background on ordinary differential equations.

Schedule

  • Tuesday 18 February 2025, 9:30-12:30
  • Wednesday 19 February 2025, 9:30-12:30
  • Tuesday 25 February 2025, 9:30-12:30
  • Wednesday 26 February 2025, 9:30-12:30

If you want to attend the course via Microsoft Teams, please write to ().

The course is offered by the PhD course in Mathematical and Physical Sciences of the University of Udine.
Course page: https://dmif.uniud.it/it/didattica/dottorato/smf/offerta-didattica/2024-2025/continuation-and-bifurcation-analysis-of-dynamical-systems.